Let G(V, E) be a graph with n-vertex-set V and m-edge-set E. Meanwhile, each vertex v is associated with a nonnegative weight W(v). Given a subset F of V, this paper studies the problem of finding a perfect dominating set D such that δ(D) = ∑ is minimized under the restriction that D ⊆ (V F). The vertices in F are called forbidden vertices. We first define a new class of graphs, called l ∈D v D...

Gustedt, J., On the pathwidth of chordal graphs, Discrete Applied Mathematics 45 (1993) 233-248. In this paper we first show that the pathwidth problem for chordal graphs is NP-hard. Then we give polynomial algorithms for subclasses. One of those classes are the k-starlike graphs a generalization of split graphs. The other class are the primitive starlike graphs a class of graphs where the inte...

We make a survey of recent results on the geometrical properties of smooth bump functions and the geometrical and topological properties of starlike bodies in Banach spaces. We try to stress the interplay between infinitedimensional topology and nonlinear functional analysis by relating questions about topological and geometrical properties of starlike bodies to other interesting problems on no...

This article defines a new class of meromorphic parabolic starlike functions in the punctured unit disc D*={z∈C:0<|z|<1} that includes fixed second coefficients As,cdψ,τ,ν,η and q- hypergeometric functions. For function belonging to As,cdψ,τ,ν,η, some properties are obtained, including coefficient inequalities, closure theorems, radius convexity.

In recent years, the theory of operators got attention many authors due to its applications in different fields sciences and engineering. this paper, making use Bernardi integral operator, we define a new class starlike functions associated with sine functions. For our function class, extended Bernardi’s theorem is studied, upper bounds for fourth Hankel determinant are determined.

The main objective of this paper is to study a new family analytic functions that are q-starlike with respect m-symmetrical points and subordinate the q-Janowski function. We investigate inclusion results, sufficient conditions, coefficients estimates, bounds for Fekete–Szego functional |a3−μa22| convolution properties belonging class. Several consequences results also obtained.

In the present work, authors introduce a new linear differential operator associated with $ q $-calculus which uses $-derivative operator. For class involving operator, interesting properties like coefficient inequality, growth, distortion, convolution and radii of starlikeness are established. Various connections that earlier works pointed out.

We introduce and study a new Ma–Minda subclass of starlike functions $${\mathcal {S}}^*_{\varrho },$$ defined as $$\begin{aligned} {\mathcal {S}}^{*}_{\varrho }:=\left\{ f\in {A}}:\frac{zf'(z)}{f(z)} \prec \cosh \sqrt{z}=:\varrho (z), z\in {\mathbb {D}} \right\} , \end{aligned}$$ associated with an analytic univalent function $$\cosh \sqrt{z},$$ where we choose the branch square root so that \s...

In this paper, we define a generalized class of starlike functions which are based upon some convolution operators on Hilbert space involving the Fox-Wright generalization of the classical hypergeometric pFq function (with p numerator and q denominator parameters). The various results presented in this paper include (for example) normed coefficient inequalities and estimates, distortion theorem...